The Annals of Probability

Global well-posedness of the dynamic $\Phi^{4}$ model in the plane

Jean-Christophe Mourrat and Hendrik Weber

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Abstract

We show global well-posedness of the dynamic $\Phi^{4}$ model in the plane. The model is a nonlinear stochastic PDE that can only be interpreted in a “renormalised” sense. Solutions take values in suitable weighted Besov spaces of negative regularity.

Article information

Source
Ann. Probab., Volume 45, Number 4 (2017), 2398-2476.

Dates
Received: January 2015
Revised: February 2016
First available in Project Euclid: 11 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.aop/1502438431

Digital Object Identifier
doi:10.1214/16-AOP1116

Mathematical Reviews number (MathSciNet)
MR3693966

Zentralblatt MATH identifier
1381.60098

Subjects
Primary: 81T27: Continuum limits 81T40: Two-dimensional field theories, conformal field theories, etc. 60H15: Stochastic partial differential equations [See also 35R60] 35K55: Nonlinear parabolic equations

Keywords
Nonlinear stochastic PDE stochastic quantisation equation quantum field theory weighted Besov space

Citation

Mourrat, Jean-Christophe; Weber, Hendrik. Global well-posedness of the dynamic $\Phi^{4}$ model in the plane. Ann. Probab. 45 (2017), no. 4, 2398--2476. doi:10.1214/16-AOP1116. https://projecteuclid.org/euclid.aop/1502438431


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